Hi, dev here. I certify you that the physics are OKish. You should burn at apoapsis to circularize, etc. What prevent you to realize this is that it's hard to know when you're at apo/periapsis, so you're burning with some vertical velocity and that changes how your orbit change. Anyway, this game was really a joke, if you want an educational game, I've also made this: http://deltav.corpsmoderne.net/